IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v81y2016i3d10.1007_s11336-015-9491-8.html
   My bibliography  Save this article

Comparing Latent Means Without Mean Structure Models: A Projection-Based Approach

Author

Listed:
  • Lifang Deng

    (Beihang University)

  • Ke-Hai Yuan

    (University of Notre Dame)

Abstract

The conventional setup for multi-group structural equation modeling requires a stringent condition of cross-group equality of intercepts before mean comparison with latent variables can be conducted. This article proposes a new setup that allows mean comparison without the need to estimate any mean structural model. By projecting the observed sample means onto the space of the common scores and the space orthogonal to that of the common scores, the new setup allows identifying and estimating the means of the common and specific factors, although, without replicate measures, variances of specific factors cannot be distinguished from those of measurement errors. Under the new setup, testing cross-group mean differences of the common scores is done independently from that of the specific factors. Such independent testing eliminates the requirement for cross-group equality of intercepts by the conventional setup in order to test cross-group equality of means of latent variables using chi-square-difference statistics. The most appealing piece of the new setup is a validity index for mean differences, defined as the percentage of the sum of the squared observed mean differences that is due to that of the mean differences of the common scores. By analyzing real data with two groups, the new setup is shown to offer more information than what is obtained under the conventional setup.

Suggested Citation

  • Lifang Deng & Ke-Hai Yuan, 2016. "Comparing Latent Means Without Mean Structure Models: A Projection-Based Approach," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 802-829, September.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-015-9491-8
    DOI: 10.1007/s11336-015-9491-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-015-9491-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-015-9491-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    2. Robert Jennrich & Albert Satorra, 2013. "Erratum to: Continuous orthogonal complement functions and distribution-free goodness of fit tests in moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 553-553, July.
    3. Robert Jennrich & Albert Satorra, 2013. "Continuous Orthogonal Complement Functions and Distribution-Free Goodness of Fit Tests in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 545-552, July.
    4. Ke-Hai Yuan & Peter Bentler & Wai Chan, 2004. "Structural equation modeling with heavy tailed distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 421-436, September.
    5. Michael Browne & Alexander Shapiro, 2015. "Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 196-199, March.
    6. James Anderson & David Gerbing, 1984. "The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 155-173, June.
    7. repec:ucp:bkecon:9780226316529 is not listed on IDEAS
    8. Kenneth A. Bollen & Robert A. Stine, 1992. "Bootstrapping Goodness-of-Fit Measures in Structural Equation Models," Sociological Methods & Research, , vol. 21(2), pages 205-229, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael Browne & Alexander Shapiro, 2015. "Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 196-199, March.
    2. Albert Satorra & Heinz Neudecker, 2015. "A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 938-948, December.
    3. Robert Jennrich & Albert Satorra, 2016. "The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 90-101, March.
    4. Johan Oud & Manuel Voelkle, 2014. "Do missing values exist? Incomplete data handling in cross-national longitudinal studies by means of continuous time modeling," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3271-3288, November.
    5. Liat Ayalon, 2018. "Perceived Age Discrimination: A Precipitator or a Consequence of Depressive Symptoms?," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 73(5), pages 860-869.
    6. Ihsana Sabriani Borualogo & Ferran Casas, 2023. "Bullying Victimisation and Children’s Subjective Well-being: A Comparative Study in Seven Asian Countries," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 16(1), pages 1-27, February.
    7. Shelley H. Liu & Yitong Chen & Jordan R. Kuiper & Emily Ho & Jessie P. Buckley & Leah Feuerstahler, 2024. "Applying Latent Variable Models to Estimate Cumulative Exposure Burden to Chemical Mixtures and Identify Latent Exposure Subgroups: A Critical Review and Future Directions," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(2), pages 482-502, July.
    8. Luke Butcher & Ian Phau & Min Teah, 2016. "Brand prominence in luxury consumption: Will emotional value adjudicate our longing for status?," Journal of Brand Management, Palgrave Macmillan, vol. 23(6), pages 701-715, November.
    9. Enno Siemsen & Kenneth A. Bollen, 2007. "Least Absolute Deviation Estimation in Structural Equation Modeling," Sociological Methods & Research, , vol. 36(2), pages 227-265, November.
    10. Janina Isabel Steinert & Lucie Dale Cluver & G. J. Melendez-Torres & Sebastian Vollmer, 2018. "One Size Fits All? The Validity of a Composite Poverty Index Across Urban and Rural Households in South Africa," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(1), pages 51-72, February.
    11. Paul MUKUCHA & Divaries Cosmas JARAVAZA & Forbes MAKUDZA, 2022. "Towards Gender-Based Market Segmentation: The Differential Influence of Gender on Dining Experiences in the University Cafeteria Industry," Management and Economics Review, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 7(2), pages 182-200, June.
    12. Shuli Gao & Yanli Guo & Jianbin Chen & Lin Li, 2016. "Factors affecting the performance of knowledge collaboration in virtual team based on capital appreciation," Information Technology and Management, Springer, vol. 17(2), pages 119-131, June.
    13. Mansoora Ahmed & Sun Zehou & Syed Ali Raza & Muhammad Asif Qureshi & Sara Qamar Yousufi, 2020. "Impact of CSR and environmental triggers on employee green behavior: The mediating effect of employee well‐being," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 27(5), pages 2225-2239, September.
    14. Amber Mosewich & Valerie Hadd & Peter Crocker & Bruno Zumbo, 2013. "Invariance Testing of the SF-36 Health Survey in Women Breast Cancer Survivors: Do Personal and Cancer-related Variables Influence the Meaning of Quality of Life Items?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 110(2), pages 559-577, January.
    15. Wen Tang & Xiangyang Zhang & Youyi Tian, 2023. "Investigating Lifelong Learners’ Continuing Learning Intention Moderated by Affective Support in Online Learning," Sustainability, MDPI, vol. 15(3), pages 1-18, January.
    16. Sharifah Rahama Amirul & Khairul Hanim Pazim & Sharifah Milda Amirul & Rasid Mail & Jakaria Dasan, 2022. "Developing and validating the qualitative labour productivity measurement in service industry," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(4), pages 2853-2874, August.
    17. María Luisa Pajuelo Moreno & Teresa Duarte-Atoche, 2019. "Relationship between Sustainable Disclosure and Performance—An Extension of Ullmann’s Model," Sustainability, MDPI, vol. 11(16), pages 1-33, August.
    18. Stéfanie André, 2014. "Does Trust Mean the Same for Migrants and Natives? Testing Measurement Models of Political Trust with Multi-group Confirmatory Factor Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 115(3), pages 963-982, February.
    19. Kroh, Julia & Globocnik, Dietfried & Schultz, Carsten & Holdhof, Frederike & Salomo, Søren, 2024. "Micro-foundations of digital innovation capability – A mixed method approach to develop and validate a multi-dimensional measurement instrument," Technological Forecasting and Social Change, Elsevier, vol. 198(C).
    20. Francisco J. Conejo & Lawrence F. Cunningham & Clifford E. Young, 2020. "Revisiting the Brand Luxury Index: new empirical evidence and future directions," Journal of Brand Management, Palgrave Macmillan, vol. 27(1), pages 108-122, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-015-9491-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.